The AC tachogenerator is used to measure the speed only in one direction. In AC tachogenerator the armature is provided with an AC winding, either single phase or three phase windings.
When the rotor is stationary and primary winding excited by an AC input voltage, the induced voltage in secondary is zero. Due to relative position of two winding being placed at 900 to each other. As the rotor rotates, a voltage is induced in the secondary winding whose magnitude is propertional to the rotor speed.
The emf induced in quadrature coil is directly proportional to the rotor speed and is in phase with applied voltage to the refrence coil.
Vt = Ktɸ (t)
Kt = tachogenerator constant.